考虑泊松效应的材料/结构一体化设计方法

A concurrent design method for microstructures of materials and macrostructures by considering the Poisson effect

为实现含有不同泊松比组分复合材料的优化设计,并考虑宏观结构及复杂的边界条件,提出了考虑泊松效应的材料/结构一体化设计方法,其显著特征在于不同组分材料中引入了泊松比插值,假设宏观结构由周期性排列的复合材料组成,复合材料含两种各向同性且泊松比不同的组分材料,以静态问题中柔顺度最小化或动态问题中特征值最大化为目标以及宏微观体积比为约束建立了拓扑优化模型。采用均匀化理论预测了复合材料等效性能,推导了目标函数对宏微观密度变量的敏度表达式。分别采用密度过滤和敏度过滤来消除宏微观拓扑优化中的不稳定性现象。采用优化准则法分别更新宏观、微观密度变量,考察了微观体积比和组分材料泊松比参数对优化结果的影响。三维数值算例结果表明所提出的一体化方法具有可行性和优越性。

For optimal design of the composite composed of material with different Poisson＇s ratios, a concurrent design method for microstructures of composites and macrostructures by considering the Poisson effect was presen- ted, when considering the macrostructure and complicated boundary conditions. A distinctive feature lies in the in terpolation of Poisson＇s ratios for different constituent phases. The macrostruetures were supposed to be construc ted by periodic base composites which contains two isotropic constituent phases with distinct Poisson＇s ratios. The topological optimization model was established where the system compliance was minimized in static problems or the eigenvalue was maximized in dynamic problems and the macro and micro scale volume fraction was used as con straints. The effective properties of the composites were calculated through the homogenization theory. Sensitivities on macro and micro scales level were derived. Density filter and sensitivity filter schemes were adopted to eliminate the instabilities in macro and micro-scale topology optimization, respectively. The optimality criteria method was used to update both the macro-and micro scale densities. The effect of the micro scale volume fraction and Poisson＇s ratio of the constitute phases on topological results was investigated. Several 3D illustrative examples were presented to demonstrate the effectiveness and advantage of the proposed concurrent design approach.